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lfunc_lfunctions • Show schema
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{'Lhash': '1724865142878633915597278465449', 'a10': [-13.480108460556886, 0.0], 'a2': [-4.082584595342656, 0.0], 'a3': [0.0, 0.0], 'a4': [8.66749697812916, 0.0], 'a5': [3.3018564945193707, 0.0], 'a6': [0.0, 0.0], 'a7': [5.576034798338615, 0.0], 'a8': [-2.725112880347884, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 88.67987073862818, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [167, [[1.0, 0], [167.0, 0]]]], 'bad_primes': [3, 167], 'central_character': '1503.1', 'coefficient_field': 'CDF', 'conductor': 1503, 'conductor_radical': 501, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.082584595342656, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.3018564945193707, 0], [125.0, 0]], [[1.0, 0], [-5.576034798338615, 0], [343.0, 0]], [[1.0, 0], [-62.04773298667054, 0], [1331.0, 0]], [[1.0, 0], [-7.809376062831507, 0], [2197.0, 0]], [[1.0, 0], [-107.52036412869741, 0], [4913.0, 0]], 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'data': '1.36067867799540901514112873400', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81881784706869627642941109302', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45062560215079658581120635662', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 88.67987073862818, 'bad_primes': [3, 167], 'central_character': '1.1', 'conductor': 1503, 'conductor_radical': 501, 'degree': 2, 'index': 162, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1503/4/a/a/1/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-1503-1.1-c3-0-162', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1503-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.41699903040391, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36067867799540901514112873400', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1724865142878633915597278465449', 'Lhash_array': ['1724865142878633915597278465449'], 'label': '2-1503-1.1-c3-0-162', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1503/4/a/a/1/2'}